7.1.4 Journal: Arithmetic Sequences Journal

Algebra I

Points Possible:20

Scenario: Swim Training

Instructions:

View the video found on page 1 of this journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations.

The Students' Conjectures: Two students, Ernest and Denise, are training for a swim half-marathon in 10 weeks, and they disagree about their training schedule. If they follow Ernest's suggested training schedule, will they be ready to swim 5 km in time for the half-marathon?

Complete the table to summarize each student's suggested training schedule. (2 points: 1 point for each row of the chart)

Classmate Conjecture

Ernest

Denise

Do the distances they swim every week make an arithmetic sequence? Why? (1 point)

Analyzing the Data:

Fill out the schedules for the first four weeks of training. (2 points: 1 point for each person)

Ernest's Schedule

Denise's Schedule

Week Kilometers to swim daily Week Kilometers to swim daily

1 1

2 2

3 3

4 4

Write the recursive formula for each sequence: an = an – 1 + d.

(4 points: 2 point for each formula)

Student

d

Recursive formula

Ernest

Denise

Find the explicit formula for each arithmetic sequence: an = a1 + (n – 1) • d.

(4 points: 2 points for each formula)

Student

Explicit formula

Ernest

Denise

Using the explicit formula, calculate how far the students will be swimming on week 10 using Ernest's schedule. (3 points)

Using the explicit formula, calculate how far the students will be swimming on week 10 using Denise's schedule. (3 points)

Making a Decision

Which training schedule will get them ready to swim 5 km in time for the half-marathon? (1 point)